Nate Smith

Potential Energy

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In physics, we are taught that an object thrown straight up begins with an amount of kinetic energy equal to 1/2mv^2 (m = mass and v = velocity). When it comes to rest at the top of its path, it has no kinetic energy, but it has an amount of potential energy equal to mgh (g = acceleration to gravity and h = height above initial position). It can be shown that the amount of kinetic energy lost equals the amount of potential energy gained, and therefore the total amount of energy is conserved. The conservation of energy (in my limited experience) seems to be a cornerstone of physics.

Is there anything problematic with saying that the energy is conserved, but only as "potential" energy? After all, a potential is not an actual. Is the conservation of energy more of an epistemological principle than a metaphysical one, or a mixture of the two?

When an object slides to rest along the floor, its kinetic energy becomes thermal energy, so in this example, the principle appears more metaphysical. I've never felt fully comfortable with potential energy though. Would someone explain the epistemological validity of potential energy and conservation of energy? Thanks.

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I've never felt fully comfortable with potential energy though. -----

I'm not sure what the difficulty is. Before a bomb explodes, where is all that energy? It's in the chemical bonds. Potential energy is physical explanation, not a metaphysical explanation. Potential simply means capable of becoming an actuality.

What kind of metaphyiscal/epistemological explanation are you looking for? A thing changes according to its nature.

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I'm not sure what the difficulty is. Before a bomb explodes, where is all that energy? It's in the chemical bonds. Potential energy is physical explanation, not a metaphysical explanation. Potential simply means capable of becoming an actuality.

What kind of metaphyiscal/epistemological explanation are you looking for? A thing changes according to its nature.

I don't have as much of a problem with the idea of potential energy as its part in the conservation of energy. We're told that energy is neither gained nor lost, it just converts from one type to another. But if kinetic energy (for example) is lost when an object travels to the top of its path, what is gained? We say that it gains potential energy, but is anything really gained?

If something is conserved, doesn't it need to be conserved as something and not just as a potential something?

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If something is conserved, doesn't it need to be conserved as something and not just as a potential something?

I've no doubt that Stephen can provide the definitive answer, but this is interesting so I'll give it a shot.

I think you're focusing too much on the historical term "potential". In actual reality, something *has* changed, the position of the object in space, after it traverses a path through spacetime that required energy to complete. In a sense, the spatial relationship of that object to the earth and its gravitational effects *does* represent the energy that it took for it to act against the force of gravity. There is nothing more metaphysical about something moving (kinetic energy) rather than having a different position in space, both are real changes. Note that the kinetic energy is no less of a "potential", too. You can't use that energy without slowing down the object in some fashion. (And because that involves (negative) acceleration, there is no doubt some deep tie to that, and an object falling back to earth, in terms of the equivalence principle of General Relativity (equivalence of gravity and acceleration), but I don't know enough to comment further on that.)

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I don't have as much of a problem with the idea of potential energy as its part in the conservation of energy. We're told that energy is neither gained nor lost, it just converts from one type to another. But if kinetic energy (for example) is lost when an object travels to the top of its path, what is gained? We say that it gains potential energy, but is anything really gained?

If something is conserved, doesn't it need to be conserved as something and not just as a potential something?

I think the fundamental question you're asking is "what is energy?" To which I'm indubitably unqualified to answer. As you've defined potential energy pertaining to motion, it only applies in a gravitational field, when the direction of motion is parallel to the gravitation. An airplane moving at constant velocity has kinetic energy, but no potential energy in the direction of motion. So, as I interpret the concept of potential energy, it refers to energy that is put into a system, such as throwing a rock in the air, and can later then be changed into other forms of energy, such as breaking a glass window, or making a sound when the rock hits the ground, or simply being converted back to kinetic energy by falling down.

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Note that the kinetic energy is no less of a "potential", too. You can't use that energy without slowing down the object in some fashion. (And because that involves (negative) acceleration, there is no doubt some deep tie to that, and an object falling back to earth, in terms of the equivalence principle of General Relativity (equivalence of gravity and acceleration), but I don't know enough to comment further on that.)

Oliver, what you bring up is something I've thought of as well and find quite fascinating, and that is that outside of some kind of potential-field, an object's kinetic energy is completely arbitrary (what claim could one make on one's kinetic energy if there were no other objects around by which to posit a personal speed?).

So I would say that not only is potential-energy positional based, but so is kinetic energy. And I think this is the source of Nate's confusion: he views (correct me if I'm wrong Nate!) that when an object gains kinetic energy, it is physically gaining some kind of observable energy or quantity, but however when it enters a potential field and gains potential-energy it is difficult to imagine what energy the object has "gained".

That's why I think it would be better to view both kinetic- and potential-energy as positional-based on one's relation between different object's and fields. We can't describe what energy a ball has gained when falling without discussing the work that has been done on it by the field, and we can't describe the work done without defining some clear positional-interval through which the ball has passed :)

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To clarify a bit more of what I said:

Nate, when we say that an object gains kinetic or potential-energy, I don't think you should take it to mean that the object has gained some kind of physical quantity that can be measured irrelevant to the surroundings in which it inhabits.

I don't think I would even say that kinetic- or potential-energy is a quantity that an object can inherently possess, gain, or lose. I think that the only way by which kinetic or potential-energy can be defined is by relation to other objects; and that when we say something has "gained" potential or kinetic energy, it really hasn't "gained" any quantity inherent to the object, but rather its position with respect to other objects and fields has changed.

When you hurl a ball into the air, it has gained a kinetic energy. What specific kinetic energy? You can only specify that by observing the speed at which the position of the ball changes with respect to your position in space. So the ball really hasn't "gained" anything, only its positional-relationship to you has changed.

When the ball is slowed down to a peak-height by gravity, it has gained a potential energy. What potential energy? You can only specify that by measuring the interval of distance the ball has traveled through the gravitational field of the Earth. So once again, the ball hasn't really gained anything, it is simply in a different position relative to the gravitational field it inhabits.

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Is there anything problematic with saying that the energy is conserved, but only as "potential" energy? After all, a potential is not an actual. Is the conservation of energy more of an epistemological principle than a metaphysical one, or a mixture of the two? ...

When an object slides to rest along the floor, its kinetic energy becomes thermal energy, so in this example, the principle appears more metaphysical. I've never felt fully comfortable with potential energy though. Would someone explain the epistemological validity of potential energy and conservation of energy?

Potential energy, in your context of basic mechanics, is the potential to do work on an object by virtue of its position and in accordance with a force that may also vary with position. The positions and the forces are physical; the potential energy is an abstraction based on them, in just the way it is described in basic physics books, which you already understand.

In looking for a more philosophical understanding about the cognitive nature of the physics, if you look for a metaphysical "entity" or the equivalent of a direct metaphysical concrete for every concept of physics you will not find it. The science of physics uses a hierarchy of abstract concepts and principles. They refer to reality, but for high level abstractions you have to know how they do so down through the hierarchy embracing different concepts of different physical attributes taken in some combination. That is the key you are looking for when you grasp for an understanding in terms of "metaphysics or epistemology or a mixture."

Notice also that a quantity of potential energy is relative to the frame of reference, and that what matters is the difference in potential energy. That is another clue that potential energy is a higher level abstraction and not a direct metaphysical "thing". But it is more than a mathematical method because it refers to physical concepts.

The same goes for kinetic energy: it's an abstract concept of physics based on your concepts of the physical attributes of mass and motion and how to combine them in a way related to work and potential energy.

These concepts are objective, not intrinsic or subjective. If you think of all this in terms of a hierarchy of abstract concepts instead of looking for some single metaphysical element as their referents, their basic epistemological validity will be much clearer simply using the standard text book descriptions of what they mean. (See especially the presentation in Feynman's Lectures.)

As for conservation of energy, that is a principle established inductively. It also guides the formation of the proper abstractions of the different kinds of energy so that the proper physical attributes are combined in the right way so that it all comes out right. That doesn't make it arbitrary or subjective, it gives you knowledge of how reality behaves, but to get that knowledge you have to form the right objective concepts in the right hierarchy.

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Note that the kinetic energy is no less of a "potential", too. You can't use that energy without slowing down the object in some fashion.

That's a very good point. The definition that I've seen for energy is "the ability to do work or change". I'm sure there are much better and broader definitions, but for the context of basic mechanics, that seems to be a good start. Given this definition, kinetic energy, as you point out, is no more than a potential to do work on other objects. In doing this work, it loses its energy.

The kinetic energy of a book sliding to rest along a floor is lost to thermal energy, which is another type of kinetic energy, or another potential ability to do work on other things, etc.

So I would say that not only is potential-energy positional based, but so is kinetic energy. And I think this is the source of Nate's confusion: he views (correct me if I'm wrong Nate!) that when an object gains kinetic energy, it is physically gaining some kind of observable energy or quantity, but however when it enters a potential field and gains potential-energy it is difficult to imagine what energy the object has "gained".

I agree, that is a mistake I was making. The idea of energy being relational is very helpful.

Potential energy, in your context of basic mechanics, is the potential to do work on an object by virtue of its position and in accordance with a force that may also vary with position. The positions and the forces are physical; the potential energy is an abstraction based on them, in just the way it is described in basic physics books, which you already understand.

In looking for a more philosophical understanding about the cognitive nature of the physics, if you look for a metaphysical "entity" or the equivalent of a direct metaphysical concrete for every concept of physics you will not find it. The science of physics uses a hierarchy of abstract concepts and principles. They refer to reality, but for high level abstractions you have to know how they do so down through the hierarchy embracing different concepts of different physical attributes taken in some combination. That is the key you are looking for when you grasp for an understanding in terms of "metaphysics or epistemology or a mixture."

Well said. Thanks all for the comment, very helpful.

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